The Sages teach that “Elul” is an acronym for the verse in Song of Songs: “I am my Beloved’s and my Beloved is mine.”
“Beloved” demonstrates a relationship and feeling of love, in which G-d declares openly: “Israel is my young one and I love him.” Even the smallest Jewish child is educated to be constantly aware that G-d is his very best friend.
In the same spirit, each of the four words of this verse end with the letter Yud. Numerically, the four Yuds together equal 40, corresponding to the 40 days between the first of Elul and Yom Kippur. By the time Yom Kippur arrives, G-d looks upon the Jews as holy angels. Even as they live in physical bodies, they wear untainted garments – which is why they wear white on Yom Kippur – demonstrating that they are cleansed of anything contrary to G-d’s will. And even if there was at one time a “stain,” the spiritual toil before Elul surely erased any stains, and even more so, transformed them to be “white as snow.”